Intuitively, the tree-width function, \(\operatorname{\mathbf {tw}}: \mathcal {G} \rightarrow \mathbb {N}\)  measures how far a given graph is from being a tree. For example, edge-less graphs have tree-width 0, forests with at least one edge have tree-width 1 and, for \(n > 1\) , \(n\) -vertex cliques have tree-width \(n-1\) . Tree-width was introduced independently by many authors [1]}, [2]}, [3]} and thus has many equivalent definitions; the most common definition makes use of the related concept of a tree-decomposition. Here we give its definition for hypergraphs [4]}.
